3 comments

I do not thing that substituting limits is actually allowed, since the limit is 0, thus, 1/L = infinity? This is undefined, by Apostol theorem, where it is allowed to apply limit quotient rule only if the denominator is not zero.

The way to solve this is to use the upper bound of 1/n. The adventurer needs to show that x_n <= 1/n. This can be done by induction. After this use the squeeze theorem 0 <= x_n <= 1/n, which shows that the limit is zero.